Fibonacci Calculator

About this tool

What Is the Fibonacci sequence? Fibonacci Calculator. The Fibonacci calculator returns the n-th Fibonacci number exactly, using big-integer arithmetic even at position 1000. You also get the sum of the first n terms and the ratio between consecutive terms that approaches the golden ratio. The sequence starts with F(0) = 0 and F(1) = 1; every later term is the sum of the two previous ones: F(n) = F(n−1) + F(n−2). So the opening terms are 0, 1, 1, 2, 3, 5, 8, 13, 21 and 34. The pattern appears in plant growth, shell spirals, and financial chart analysis, and the ratio F(n)/F(n−1) settles closer and closer to φ ≈ 1.618 as n grows. F(n) = F(n−1) + F(n−2), with F(0) = 0 and F(1) = 1. How to Use Enter a position from 1 to 1000 in the Position field. Read F(n), the sum of the first n terms, and the ratio to the previous term. For positions up to 40 the terms are listed visually in the breakdown. Worked Example Enter 10. The tool returns F(10) = 55 and the sum of the first 10 terms, 143. The ratio 55/34 ≈ 1.6176 already sits close to the golden ratio. At position 50 the result is 12586269025. Common Use Cases algorithm exercises and coding interviews teaching recursion and sequences estimating market retracement levels exploring nature's number patterns Important Notes Results use exact integer arithmetic, with no loss at large positions. The position is treated as 1-indexed: position